CAT Quantitative Aptitude Questions | CAT Geometry - Mensuration Problems

CAT Questions | CAT Mensuration Questions | Spheres and Cubes

This question is from CAT Mensuration in CAT Geometry. In this question, there is a sphere shaped object placed insida a cube and an object tries to reach it from its vetices and we need to find the minimum distance to reach the object inside the sphere with the given conditions. Mensuration Questions in the CAT exam can be solved with practical approach and thought process rather than just knowing theorems from CAT Geometry. Even if one is not completely prepared for CAT Geometry exam, he or she should be able to do well in Mensuration problems tested by the CAT Exam. Knowing Mensuration formulas is important. Make sure you master Mensuration questions for CAT exam. This is one of the questions which looks difficult on first look but with a little visualization and concept, can be cracked in a minute. This kind of question is more likely to appear in CAT.

Question 10: A spherical shaped sweet is placed inside a cube of side 5 cm such that the sweet just fits the cube. A fly is sitting on one of the vertices of the cube. What is the shortest distance the fly must travel to reach the sweet?

  1. 2.5 cm
  2. 5(√3 – 1) cm
  3. 5(√2 – 1) cm
  4. 2.5(√3 – 1) cm

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Explanatory Answer

Method of solving this CAT Question from Geometry - Mensuration: The question demands visualization. The shortest distance required to be travelled by the fly would be diagonally and be given by:-

Diagram :
CAT : Geometry: Mensuration; Spheres and Cubes
Distance = \\frac{(Diagonal of cube – Diameter of sphere)}{2}\\)
= \\frac{(5√3 - 5)}{2}\\) (Since diagonal of the cube is given as √3 x l)
= \\frac{5(√3 - 1)}{2}\\)
= 2.5(√3 – 1)

The question is "What is the shortest distance the fly must travel to reach the sweet? "

Hence, the answer is 2.5(√3 – 1) cm

Choice D is the correct answer.


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